Thermal Properties of Matter

Thermal expansion

$Δ L = Lα Δ T,$ $Δ A = A β Δ T,$ $Δ V = V γ Δ T$
$α : β : γ = 1 : 2 : 3$
Pendulum clock
$Δ t = \frac{1}{2} α Δ T \times t$ (time lost per $t$ when hotter)
Temperature scales
$\frac{C}{100} = \frac{F - 32}{180} = \frac{K - 273.15}{100}$

Conduction
$\frac{d Q}{d t} = \frac{K A Δ T}{L},$ $R_{th} = \frac{L}{K A}$
Series and parallel
$R = R_{1} + R_{2}$ (series) $,$ $\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}}$ (parallel)
Stefan–Boltzmann
$P = e σ A T^{4};$ $P_{net} = e σ A (T^{4} - T_{0}^{4})$
Wien's law
$λ_{m} T = b \approx 2.9 \times 1 0^{- 3}$ m K
Newton's law of cooling
$\frac{d T}{d t} = - k (T - T_{0});$ $\frac{T _{1} - T _{2}}{t} \approx k (\frac{T _{1} + T _{2}}{2} - T_{0})$